Focused sequent calculi appeared initially in the Andreoli's work on linear
logic [1]}. The author identified a subset of proofs from
Gentzen-style sequent calculus, which is complete and tractable.
[2]} proposed the focused sequent calculi \(\mathbf {LJF}\) 
where they used a mapping of \(\mathbf {Int}\)  into linear logic and adapted the Andreoli's
system to work with the image. [3]} presented the focused system
\(\mathbf {LJQ}\)  that work direct in \(\mathbf {Int}\) . Focusing is used in their
system as a way to implement restrictions in the \(\rightarrow \) -left rule as proposed by
[4]} and [5]}. The work of [3]}
follows from the calculus with the same name presented in [7]}.
